Solve for $x$ and $y$ using substitution. ${-2x-5y = 7}$ ${y = -3x+9}$
Since $y$ has already been solved for, substitute $-3x+9$ for $y$ in the first equation. ${-2x - 5}{(-3x+9)}{= 7}$ Simplify and solve for $x$ $-2x+15x - 45 = 7$ $13x-45 = 7$ $13x-45{+45} = 7{+45}$ $13x = 52$ $\dfrac{13x}{{13}} = \dfrac{52}{{13}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = -3x+9}\thinspace$ to find $y$ ${y = -3}{(4)}{ + 9}$ $y = -12 + 9$ $y = -3$ You can also plug ${x = 4}$ into $\thinspace {-2x-5y = 7}\thinspace$ and get the same answer for $y$ : ${-2}{(4)}{ - 5y = 7}$ ${y = -3}$